The rigid catenary is an important component in transmitting electricity to the trains operating in underground tunnels. Stability of the contact force is one of the key indicators of reliable power transmission, which is directly influenced by the vibration response of the catenary. The purpose of this paper is to study the influence of two features on the free vibration and forced vibration simulated responses of the rigid catenary: the pre-sag, representing the vertical deformation of the catenary due to its self-weight, and the staggering, which is the deformation of the catenary in the lateral direction, designed to distribute wear uniformly across the pantograph strip. Free and forced response studies are adopting realistic ranges of span lengths and support stiffnesses. Free wave propagation analysis is conducted using a wave finite element model, accounting for one periodic cell of the rigid catenary system, in which the deflection of the central span in a rigid catenary section, modelled using finite elements, is included to account for the pre-sag. The forced response studies consist of moving load and moving pantograph analyses in the basis of the same rigid catenary model used to find the pre-sag induced deflection adopted in the wave propagation study. Analysis of the results reveals important differences between the free wave propagation study and the moving load analyses, as in the latter, the significant influence of the pre-sag is visible, especially at high speeds of the moving load. A case study done using non-moving harmonic loading revealed three reasons as to why this inconsistency in the results exists: accumulation of errors due to wave propagation through multiple periodic cells, the effect of wave reflections from the section ends, and non-vertical load application with respect to the local coordinate system of the finite elements of the catenary with pre-sag. The moving pantograph study involving normative recommended three-DOF pantograph model indicates clear sensitivity of the contact forces towards pre-sag, especially at larger span lengths, showing higher standard deviation values and increased maximum contact forces. In contrast, the effect of staggering when considering a pantograph model that follows the normative recommendations is found to be insignificant throughout all the case studies presented.

The first author would like to thank the financial support provided by the FI-2022 (reference 2022 FI_B 00169), funded by the Departament de Recerca i Universitats de la Generalitat de Catalunya .

Peer Reviewed